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Day 62: Thankful Times

Today was assessment day just before Thanksgiving Break.  I hate to have assessments on the day before a break, but in AP Stats, the kids actually voted to move the test to Wednesday and they promised to show up…which they did!  I am so thankful for these kids ‘cuz they are honorable and interested young people.  This test was on probability and it seems they either “get it” or they don’t.  I may have to consider a test re-take option based on the standards of the chapter and the AP curriculum, but I need to ruminate on it for a day or two.  Students are doing homework and most of the class notes, but I think some students aren’t using them to make sure they really understand the material.  This may be because they don’t know how to use homework as a tool for deep and authentic learning, so I’ll need to consider how to develop this important and leveraging study skill with seniors who think they know it all (tongue in cheek and smile on my face).


In precalculus there was a quiz after a discussion around the opener:  Given the portion of a sinusoidal function at the right, state its critical attributes, and then write its equation in terms of cosine and sine.

Unfortunately we had slightly shorter periods due to early release, so timing was an issue in one of my classes.  They did a really nice job on the quiz, even on this cool question:  Find the average rate of change between the two points on f(x)= sin(x).

Trig Assessment Graph

A few were confused about what the “average rate of change” was asking (but this is critical for next year’s experience in Calculus) and small number of others forgot what the output of the function f(x) = sin(x) is the ratio for the input angle, but overall the rest of the kiddos nailed this problem “even though they had not seen one like this before.”  After the quiz, they asked and were smacking their foreheads knowing they “should have known that.”

I truly believe it is critically important for kids to actually transfer learning in unfamiliar settings…and I preach it daily.   I almost always ask a question that they “haven’t seen before” but uses only those concepts and processes they have practiced a great deal.  I tell them that I can’t ask them anything that they don’t have the tools to approach and find an answer, but they may have to use their knowledge in a new way which requires them to really understand the concepts underlying the process they are learning. And they are beginning to embrace the expectation.  I am so thankful for that willingness to stretch and learn and retain that my precalculus students are growing into this year!

Happy Thanksgiving!  What are you thankful for this year?

Day 36: Two Truths and a Lie

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It was game time in Precalculus.  My precalc teaching partner and I thought it was time to jazz things up a little while reinforcing previously learned topics through meaningful discussion.  So we thought we’d present to the class a True-False question and have them move to the true or false sides of the room and then debate.  But we soon thought what would happen if everyone went to one side and there was not real discussion. We thought, “we need a game,” and Two Truths and a Lie immediately came to mind.  We used the Connelly, Hughes-Haslett Functions Modeling Change chapter review true-false questions as our guide, divvied up the work and came up with 16 sets of three statements.  Then we laminated them as cards and presented the game, math-style!  Each group got a different card to start with and the group needed to determine the true and false-ness of each choice.  They gained a point if their answer was correct AND justified correctly (awh…the 3rd math practice at work!).  If they answered wrong or defended incorrectly, they lost a point and had to go back and work to get the correct answer.  I would randomly select who would argue/defend their choice or ask them to defend a true statement.  Once the answer was correct and defended accurately, they returned the card to the selection pile and chose another card.  The energy level was high, the discussions were intellectually intense and the defending was awesome.

Day 35: Math words mean something…specific


I so love having my CCSS magnetized 8 Practice words ready to use.  After grading the quiz on rational functions, I realized I needed to make sure students were clear about the words expression and equation..drives me batty!!  They were consistently writing an expression for a required equation.  That is, they didn’t include the y = or f(x) = when asked to write the equation of something.  I believe that if we teachers don’t require students to be precise in their application of words and hold them to the meaning of the words, even in lower grades, gross misconceptions can take hold which are very difficult to unhook to the students’ understanding.  How do you reinforce precise language and notation in your classroom?

Day 33: Mixture Mania


Today in Precalc we looked at various ways rational functions can appear in real world situations.  One of the more common ways is mixture problems which we talked about yesterday, you know give the problem and look at all of the different approaches students take and then help them compare strategies to determine the most efficient approach.  So as our opener problem today, the kids did this problem:  How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?  One student presented his solution on the board, but it was apparent by the student discussion that many students weren’t getting why the 0.7x was added to the numerator and a 1x (instead of a .3x) to the denominator.  So we made a model of the situation and “experimented” with a couple of friendly values to see what happened, followed by relating it to the problem.  I tried to use color to enhance the connections, but am not sure if it helped.  I do love, Love, LOVE my laminated CCSS magnet signs for the 8 practices….so convenient for highlighting how students used the practices!!  How do you help students understand the concept underlying the idea of mixture problems?

Day 7: Common Core and the 8 Practices in Action

Last year in my Precalculus course, I decided I needed to really emphasize the 8 Practices as a way to approach unfamiliar and,to students, “scary” problems.  This year I used a problem I call the Crop Duster problem based on a problem I found online at the University of Washington Math 120 Precalculus site…they actually share their textbook  (written by David Collingwood) and it has some really cool (a.k.a rich) problems. I introduced the math practices through a foldable by having the students in groups of four read two of the eight practices to themselves, and then summarize to their group.

crop duster20140910_115133[1]

Then we focused on “making sense of the problem” and “looking for structures” by having the information and the diagram available to students, but no questions.  Students were asked to generate a list of what they knew and what concepts from previous courses might apply to the problem (since we really didn’t know what the question was yet).  Love how the student embrace a tough problem easily when there is no question to distract them!!  How do you introduce the CCSS math practices to your students


Day -4: CCSS Practice and Practices

Practice vs Practices

Worked with my course partner to develop an introduction to the 8 Math Practices in our precalculus course for the first week of school.  We’re using the task as a way to get the kids talking about the practices (we’ll do some problem-solving activities in the 2nd week of the course with the practices) while introducing them to group work responsibilities using the Complex Instruction model.  With the poster*, I wanted to plant the seed regarding the difference between math practice and math practices; math practice is about developing skills whereas math practices is about mathematical habits of mind. Any-hoo, here it is:

Task: The 8 Mathematical Practices

This task is about thinking and doing work like a mathematician!  The goal is to become familiar with the eight mathematical practices.

  • Resource Manager:  Find and hand out the Math Practices foldable.  Make sure each person in the group cuts out and folds the Math Practices foldable correctly.
  • Facilitator:  Assign one member to teach two of the eight practices from the foldable.  Discuss what each might mean in Honors Precalculus.  You might also search “Common Core Mathematical Practices” with your iPad for additional details about them.
  • Team Captain:  Once the group has shared what the 8 practices are, have each member rate their ability to do each practice using Fist to 5:  fist = can’t do this practice….5 = superstar at this practice.  Find the average for each practice.
  • Recorder/Reporter:  Have each person write down their personal rating next to the practice in their packet.  Record the group average for each practice in the assigned location.  Look around the room to find it.

*I’ve looked through so many sites, and I can’t find where I originally got the poster pictured above….I want to give credit where credit is due, so if the poster is yours, PLEASE let me know so I can give you credit!!

Day -10: I’m a Math Practices Groupie

Oh my gosh.  For the last couple of weeks, I’ve been thinking about (actually agonizing over) what to present at the 2015 T3 International Conference in Fort Worth, TX….should I recycle an old talk (easy but not challenging me to grow professionally) or create a new talk (scary but forcing me to grow my practice during the year).  At 4 o’clock today (yes, the procrastination bug bit me), I finally decided to do a new talk entitled: “Fostering a Math Practices Mindset.” The idea has been fermenting, like a good wine, most of the summer, but it all came together as I was navigating rush hour traffic after the first day at a great workshop (more to come about that tomorrow, I promise).  I kinda like the title, don’t you? I finally submitted my proposal at the 11th hour.

T3 Proposal

Here’s my descriptor:

If you hear yourself say, “I know how to implement  the CCSS curriculum but I’m not sure how to get my student to know and use the math practices,” this is the session for you! Using “old school” (paper and pencil, whiteboards, etc) and “new school” ( Nspire Navigator, GoogleForms, etc) techniques, guide your students to learn and masterfully use mathematics through the CCSS Math Practices.  Experience a variety of classroom tested activities that foster your students’ Math Practices Mindset: to recognize, expertly use, reflect upon, value, and internalize the 8 Math Practices.

OK, so I’m officially a Math Practices “groupie!”  I passionately believe that the Math Practices are the real reason we teach mathematics to all students.  Granted, the skills and procedures of mathematics are beautiful, necessary for progress, and besides, I love teaching them.  But the reality is that not all kids need to know how to determine the end-behavior asymptote for a rational function to be successful in life.  But all students will have to sense-make about their environment, notice patterns and describe them to others, reason abstractly and quantitatively, choose appropriate tools to model and solve problems or answer questions, persevere in seeking solutions to problems, logically argue a point and critique others’ arguments, and communicate accurately and precisely using good notation.  Last year, I did some cool things to help my students use the practices purposefully while pushing them to become more sophisticated in their use.  I have to sift through some of the activities while also pushing myself to create new ones for this year.  But I am excited about my self-imposed challenge.  You will see some of them in action over the year.  What are you doing to help your students connect the math practices to their everyday experiences?

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